When you have a correspondence where this remains true for all products, it's called an " isomorphism" , which is maybe the most important idea in group theory.

当你有一个对所有都成立的对应关系时，它被称为“同构” ，这可能是群论中最重要的想法。

Vaida's treatment of the verbal morphology involves a tiny handful of intriguing isomorphisms, surrounded by an impenetrable sea of assumptions and highly controversial internal reconstructions that create an illusion of systemic reconstruction where there really is none.

Vaida 对词语形态学的处理涉及极少数有趣的同构，而这些同构周则充满了难以理解的假设和极具争议的内部重建， 造成了一种系统重建的假象， 但实际上并不存在这种重建。

This particular isomorphism between cube rotations and permutations of four objects is a bit subtle, but for the curious among you, you may enjoy taking a moment to think hard about how the rotations of a cube permute its four diagonals.

立方和四个对象的排列之间的这种特殊同构有点微妙，但对于好奇的人来说， 您可能会喜欢花点时间认真思考立方的如何排列其四个对角线。

But now you're in a position to ask that question in a more sophisticated way: What are all the groups up to isomorphism, which is to say we consider two groups to be the same if there's an isomorphism between them.

但现在你可以用更复杂的方式问这个问题：所有群都达到同构的程度是什么，也就是说，如果两个群之间存在同构，我们就认为它们是相同的。